The one-dimensional path decomposition expression for the step potential and mass is formulated. The propagator is analytically determined and the limiting case m 1; m 2 → m is exactly obtained.
Département de Physique, Faculté des Sciences Exactes, Université Mentouri, Route Aïn El-Bey, Constantine, 25000, Algeria
References
[1] B. Gönül, O. Özer, B. Gönül, F. Üzgün, Mod. Phys. Lett. A 17, 2453 (2002) http://dx.doi.org/10.1142/S0217732302008514[Crossref]
[2] R. Koç, G. Sahinoğlu, Eur. Phys. J. B 48, 583 (2005) http://dx.doi.org/10.1140/epjb/e2005-00422-x[Crossref]
[3] L. Chetouani, L. Dekar, T. F. Hamman, Phys. Rev. A 52, 82 (1995) http://dx.doi.org/10.1103/PhysRevA.52.82[Crossref]
[4] A. D. Alhaidari, Phys. Rev. A 66, 04116 (2002)
[5] A. D. Alhaidari, Int. J. Theor. Phys. 42, 2999 (2003) http://dx.doi.org/10.1023/B:IJTP.0000006027.49538.16[Crossref]
[6] H. Kleinert, A. Chervyakov, Phys. Lett. A 299, 319 (2002) http://dx.doi.org/10.1016/S0375-9601(02)00606-0[Crossref]
[7] A. R. Plastino, A. Rigo, M. Casas, F. Gracias, A. Plastino, Phys. Rev. A 60, 4398 (1999) http://dx.doi.org/10.1103/PhysRevA.60.4318[Crossref]
[8] V. Milanovic, Z. Ikanovic, J. Phys. A-Math. Gen. 32, 7001 (1999) http://dx.doi.org/10.1088/0305-4470/32/40/307[Crossref]
[9] B. Roy, P. Roy, J. Phys. A-Math. Gen. 35, 3961 (2002) http://dx.doi.org/10.1088/0305-4470/35/17/310[Crossref]
[10] T. O. de Carvalho, Phys. Rev. A 47, 2562 (1993) http://dx.doi.org/10.1103/PhysRevA.47.2562[Crossref]
[11] M. A. M. Aguiar, Phys. Rev. A 48, 2567 (1993) http://dx.doi.org/10.1103/PhysRevA.48.2567[Crossref]
[12] M. A. M. Aguiar, Phys. Rev. A 51, 2654(E) (1995)
[13] L. Chetouani, L. Guechi, T. F. Hammann, Y. Merabet, Nuovo Cimento B 108, 879 (1993) http://dx.doi.org/10.1007/BF02828735[Crossref]
[14] R. P. Feynmann, A. R. Hibbs, Quantum Mechanics and Path Integrals (Mc Graw-Hill, New York, 1965)
[15] H. Kleinert, Path Integrals in Quantum Mechanics Statistics and Plymer Physics (World Scientific, Singapore, 1990)
[16] C. Grosche, Phys. Rev. Lett. 71, 1 (1993) http://dx.doi.org/10.1103/PhysRevLett.71.1[Crossref]
[17] M. Acila, B. Benali, M. T. Meftah, J. Phys. A-Math. Gen. 39, 1357 (2006) http://dx.doi.org/10.1088/0305-4470/39/6/009[Crossref]
[18] J. M. Yearsley, J. Phys. A-Math. Theor. 41, 285301 (2008) http://dx.doi.org/10.1088/1751-8113/41/28/285301[Crossref]
[19] A. Auerbach, S. Kivelson, Nucl. Phys. B 257, 799 (1985) http://dx.doi.org/10.1016/0550-3213(85)90377-3[Crossref]
[20] H. A. Fertig, Phys. Rev. B 47, 1346 (1993) http://dx.doi.org/10.1103/PhysRevB.47.1346[Crossref]
[21] L. S. Schulman, R. W. Ziolkowski, In: V. Sa-yakanit et al. (Eds.), Path Integrals from mev to Mev, Jan. 1989, Bangkok, Thailand (World Scientific, Singapore 1989) 253
[22] A. Aurebach, L. S. Schulman, J. Phys. A-Math. Gen. 30, 5993 (1997) http://dx.doi.org/10.1088/0305-4470/30/17/010[Crossref]
[23] O. von Roos, Phys. Rev. B 27, 7547 (1983) http://dx.doi.org/10.1103/PhysRevB.27.7547[Crossref]
[24] J. Thomsen, G. T. Einevoll, P. C. Hemmer, Phys. Rev. B 39, 12783 (1989) http://dx.doi.org/10.1103/PhysRevB.39.12783[Crossref]
[25] A. Laissaoui, L. Chetouani, Acta Phys. Slovaca 4, 425 (2006)
[26] R. Tsu, Superlattice to Nanoelectronics (Elsevier, New York, 2005)
[27] I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals Series and Products (Acadimic, New York, 1980)